%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD064-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:10:58 AM UTC 2026
% Result : Unsatisfiable 19.94s 2.97s
% Output : CNFRefutation 19.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 24 ( 9 unt; 0 nHn; 24 RR)
% Number of literals : 48 ( 0 equ; 30 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 27 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(less_or_equal_2,negated_conjecture,
'less$uor$uequal'('additive$uidentity',a) ).
cnf(not_less_or_equal_3,negated_conjecture,
~ 'less$uor$uequal'('additive$uinverse'(a),'additive$uidentity') ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X0)
| sum('additive$uinverse'(X0),X0,'additive$uidentity') ) ).
cnf(commutativity_addition,axiom,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ) ).
cnf(well_definedness_of_additive_inverse,axiom,
( ~ defined(X0)
| defined('additive$uinverse'(X0)) ) ).
cnf(compatibility_of_order_relation_and_addition,axiom,
( ~ sum(X3,X4,X1)
| ~ sum(X2,X4,X0)
| ~ 'less$uor$uequal'(X2,X3)
| 'less$uor$uequal'(X0,X1) ) ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c1,plain,
'less$uor$uequal'('additive$uidentity',a),
inference(clausification,[status(esa)],[less_or_equal_2]) ).
cnf(c2,plain,
~ 'less$uor$uequal'('additive$uinverse'(a),'additive$uidentity'),
inference(clausification,[status(esa)],[not_less_or_equal_3]) ).
cnf(c5,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_addition]) ).
cnf(c6,plain,
( ~ defined(X0)
| sum('additive$uinverse'(X0),X0,'additive$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_addition]) ).
cnf(c7,plain,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_addition]) ).
cnf(c17,plain,
( ~ defined(X0)
| defined('additive$uinverse'(X0)) ),
inference(clausification,[status(esa)],[well_definedness_of_additive_inverse]) ).
cnf(c26,plain,
( ~ sum(X3,X4,X1)
| ~ sum(X2,X4,X0)
| ~ 'less$uor$uequal'(X2,X3)
| 'less$uor$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[compatibility_of_order_relation_and_addition]) ).
cnf(d0,plain,
( ~ defined(X0)
| sum(X0,'additive$uinverse'(X0),'additive$uidentity') ),
inference(resolution,[status(thm)],[c7,c6]) ).
cnf(d1,plain,
( ~ defined(X0)
| ~ sum(X2,X0,X1)
| ~ 'less$uor$uequal'('additive$uidentity',X2)
| 'less$uor$uequal'(X0,X1) ),
inference(resolution,[status(thm)],[c26,c5]) ).
cnf(d2,plain,
( ~ defined(X0)
| ~ 'less$uor$uequal'('additive$uidentity',X0)
| 'less$uor$uequal'('additive$uinverse'(X0),'additive$uidentity')
| ~ defined('additive$uinverse'(X0)) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( ~ 'less$uor$uequal'('additive$uidentity',a)
| ~ defined('additive$uinverse'(a))
| ~ defined(a) ),
inference(resolution,[status(thm)],[d2,c2]) ).
cnf(d4,plain,
( ~ 'less$uor$uequal'('additive$uidentity',a)
| ~ defined('additive$uinverse'(a)) ),
inference(resolution,[status(thm)],[c0,d3]) ).
cnf(d5,plain,
~ defined('additive$uinverse'(a)),
inference(resolution,[status(thm)],[c1,d4]) ).
cnf(d6,plain,
~ defined(a),
inference(resolution,[status(thm)],[d5,c17]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[c0,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD064-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 02:38:45 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.94/2.97 % SZS status Unsatisfiable for theBenchmark.p
% 19.94/2.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------